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Mirrors > Home > MPE Home > Th. List > ltaddrpd | Structured version Visualization version Unicode version |
Description: Adding a positive number to another number increases it. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
rpgecld.1 | |
rpgecld.2 |
Ref | Expression |
---|---|
ltaddrpd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpgecld.1 | . 2 | |
2 | rpgecld.2 | . 2 | |
3 | ltaddrp 11867 | . 2 | |
4 | 1, 2, 3 | syl2anc 693 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 class class class wbr 4653 (class class class)co 6650 cr 9935 caddc 9939 clt 10074 crp 11832 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 ax-resscn 9993 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-addrcl 9997 ax-mulcl 9998 ax-mulrcl 9999 ax-mulcom 10000 ax-addass 10001 ax-mulass 10002 ax-distr 10003 ax-i2m1 10004 ax-1ne0 10005 ax-1rid 10006 ax-rnegex 10007 ax-rrecex 10008 ax-cnre 10009 ax-pre-lttri 10010 ax-pre-lttrn 10011 ax-pre-ltadd 10012 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-nel 2898 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-po 5035 df-so 5036 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-ov 6653 df-er 7742 df-en 7956 df-dom 7957 df-sdom 7958 df-pnf 10076 df-mnf 10077 df-ltxr 10079 df-rp 11833 |
This theorem is referenced by: ltaddrp2d 11906 xov1plusxeqvd 12318 isumltss 14580 effsumlt 14841 tanhlt1 14890 4sqlem12 15660 vdwlem1 15685 chfacfscmul0 20663 chfacfpmmul0 20667 nlmvscnlem2 22489 nlmvscnlem1 22490 iccntr 22624 icccmplem2 22626 reconnlem2 22630 lebnumii 22765 ipcnlem2 23043 ipcnlem1 23044 ivthlem2 23221 ovolgelb 23248 ovollb2lem 23256 itg2monolem3 23519 dvferm1lem 23747 lhop1lem 23776 lhop 23779 dvcnvrelem1 23780 dvcnvrelem2 23781 pserdvlem1 24181 pserdv 24183 lgamgulmlem2 24756 lgamgulmlem3 24757 lgamucov 24764 perfectlem2 24955 bposlem2 25010 pntibndlem2 25280 pntlemb 25286 pntlem3 25298 tpr2rico 29958 omssubaddlem 30361 fibp1 30463 heicant 33444 itg2addnc 33464 rrnequiv 33634 pellfundex 37450 rmspecfund 37474 acongeq 37550 jm3.1lem2 37585 oddfl 39489 infrpge 39567 xralrple2 39570 xrralrecnnle 39602 iooiinicc 39769 iooiinioc 39783 fsumnncl 39803 climinf 39838 lptre2pt 39872 ioodvbdlimc1lem2 40147 wallispilem4 40285 dirkertrigeqlem3 40317 dirkercncflem2 40321 fourierdlem63 40386 fourierdlem65 40388 fourierdlem75 40398 fourierdlem79 40402 fouriersw 40448 etransclem35 40486 qndenserrnbllem 40514 omeiunltfirp 40733 hoidmvlelem1 40809 hoidmvlelem3 40811 hoiqssbllem3 40838 iinhoiicc 40888 iunhoiioo 40890 vonioolem2 40895 vonicclem1 40897 preimaleiinlt 40931 smfmullem3 41000 perfectALTVlem2 41631 |
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